Finite Group Databasebeta

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A4×C17×C31⋊C3 #34039070

order18972
automorphism?
homologyAbelianization (H1) = C32×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productA4×C17×C31⋊C3
unambiguous semidirect product(C22×C31⋊C3)⋊(C3×C17)
unambiguous semidirect product(A4×C31)⋊(C3×C17)
unambiguous semidirect product(C22⋊(C31⋊C3))⋊(C3×C17)
unambiguous semidirect product(C22×C17×C31⋊C3)⋊C3
unambiguous semidirect product(A4×C17×C31)⋊C3
unambiguous semidirect product(C17×C22⋊(C31⋊C3))⋊C3

Splittings

Fitting, socle, HallC22×C17×C31 ⋊ C32
derived, HallC22×C31 ⋊ C32×C17
HallC17×C31 ⋊ C3×A4
HallC22×C17 ⋊ C3×C31⋊C3
SylowC31 ⋊ C3×A4×C17
SylowC22 ⋊ C3×C17×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC17A4×C31⋊C3
commutator, cosocle, hypocenterC22×C31C32×C17
FrattiniC1G
Fitting, socleC22×C17×C31C32
LCSG ▷ C22×C31
UCSC1 ◁ C17

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2108

Conjugacy classes & character table

884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18972, 73);